Rolston, who led the Wild in goals last season, netted the game-winner early in the third period when left alone between the faceoff circles. Pierre-Marc Bouchard won a battle along the boards and slid the puck to Eric Belanger, whose pass from the corner set up Rolston's one-timer.
Minnesota goalie Josh Harding preserved the lead by stopping Michael Ryan on a breakaway with 5 minutes left and a flurry of four shots in the final minute.
Harding finished with 25 saves for Minnesota.
Phillip Gogulla had a goal and Jocelyn Thibault made 20 saves for Buffalo.
After a scoreless first period, the Wild took the lead in the first minute of the second period on a power play. Benoit Pouliot won the faceoff back to Rolston, who sent a slapshot into the far corner, over Thibault's glove.
Gogulla tied it later in the second period on the power play, after a cross-ice pass from Marek Zagrapan.
